The Rheology Handbook. Thomas Mezger

second interval, resp.)

      Example: with nH, nL, DRH and DRL as above, and DRL, 12 = 30, then:

      RBU = [(30/10) – (50/100)] / [(40/10) – (50/100)] = (3 – 0.5) / (4 – 0.5) = 2.5/3.5

      Thus: RBU = 0.71 = 71 %

      Comment: Using this simple method, usually a too high rotational speed is applied in the low-shear phase to enable regeneration conditions which are related to practice. At these conditions, which are not really simulating low-shear conditions or even the state-at-rest, any regeneration – if at all – is merely possible to a partial, very limited degree.

3.4.3Time-dependent flow behavior of samples

      showing hardening

      Rheological tests are physical tests and usually it is assumed that the chemical structure of the sample does not change during the measurement. However, if it is aimed to determine time-

      dependent flow behavior during a hardening process, e. g. during a chemical curing reaction, then both: shear conditions and measuring temperature should be kept constant (thus testing takes place at isothermal conditions). The shear load should be sufficiently low to ensure an undisturbed hardening or curing process; for example, at a shear rate of γ ̇ = 1 s-1.

      3.1.2.1.1a) Gelation time and gel time, gel point and gelation point

      An η(t)-diagram of a time-dependent hardening material usually shows a course of the viscosity curve as displayed in Figure 3.45. Here, two time points are relevant:

      1 time point tS as start time at the onset of gelation or curing reaction

      2 time point tV when reaching the previously defined viscosity value

      The terms gel time, gelation time, hardening time often are used as synonyms. Examples of measuring curves showing gelation of modified starch are displayed in [3.70]

       Figure 3.45: Time-dependent viscosity function of a sample showing gelation or curing: The

      gelation or curing reaction starts at time point tS and the previously defined viscosity value is reached at time point tV

      3.1.2.1.2Example 1: Testing epoxy resins

      1 Time point at the viscosity minimum (if it occurs): after t = 90 s (e. g. showing ηmin = 60 Pas then)

      2 Gel time (when reaching the pre-defined value of η = 100 Pas): after t = 200 s

      3.1.2.1.3Example 2: The isothermal viscosity development of reactive resin mixtures

      (acc. to DIN 16945)

      After mixing the components for 10 minutes, gelation time is determined as the period required to reach a previously defined upper limiting value of the viscosity (termed η2). The following values are specified for three different consistencies (with η1 as the viscosity directly after mixing):

      1 for η1 ≤ 250 mPas,then:η2 =1500 mPas

      2 for 250 mPas < η1 ≤ 1000 mPas,then:η2 =7500 mPas

      3 for η1 > 1000 mPas,then:η2 =15,000 mPas

      Comparsion: In ISO 2535 is stated for testing unsaturated polyester resins using a rotating bar: The gelation time is reached at the upper limiting viscosity value of 50 Pas.

      3.1.2.1.4Example 3: The gelation time of reaction resins, when reaching the thousandfold viscosity value

      The gelation time tgel is reached if ηgel = 1000 ⋅ ηmin with ηmin as the minimum viscosity. The reaction time (in min) is defined as: tr = tgel – tmin with tmin at the time point of the viscosity minimum. Measured is under isothermal conditions, e. g. using a PP-geometry (gap 0.5 mm) at a constant shear rate of 10 s-1.

      Some further, but often very simple test methods to determine whatsoever gel times or gelation times are briefly presented in Chapters 11.2.1d/e/f (formation and tackiness of resin filaments, temperature increase due to an exothermic reaction), 11.2.8e (falling ball), 11.2.11a/b (rotation until standstill) and 11.2.12a4/5/6 (reduction of an oscillation amplitude path, reaching the phase shift angle of 45°, deflection path by the formograph); see also Chapter 12 (guideline, 12.2.2, 12.2.4, 12.3.3, 12.3.5), and the Index. In Chapter 11.2.13 information can be found about the following terms: incubation time, vulcanization time, scorch time, rise time, cure time of uncured rubbers, crosslinked rubbers and elastomers.

      Note 1: Pot life , open time , and gelation time of resins

      The following terms are often used to analyze the period of time for the use of a resin in an open container at the processing temperature. The reason for the increasing gel formation may be drying, oxidation or air humidity, or a curing reaction with two-component resins. Typical evaluation by a rotational test is a viscosity measurement at a low constant shear rate, e. g. at γ ̇ = 1 s-1. Possible criteria for analysis are:

      1 The pot life is the period of time as long as a material is applicable [3.73]. In daily practice, many users are choosing the time point when the initial viscosity value has doubled.

      2 The open time is the period of time for which the material is still able to flow. This time is over if a previously defined, upper limiting value of the viscosity is reached; this time point is often also called the gelation time.

      Tip: It is more meaningful to evaluate here the viscoelastic properties using oscillatory tests (see Note 1 in Chapter 8.5.3b).

      3.1.2.1.5b) Comparison of controlled shear rate (CSR) , and controlled shear stress (CSS) tests

      For hardening or curing processes, CSR tests are involved with the disadvantage that the preset constant shear rate remains unchanged even if the viscosity values are continuously increasing and the sample is becoming more and more solid and therefore more inflexible. This can lead to irreversible partial destruction of the structure, therefore decisively disturbing a homogeneous hardening process. CSS tests offer an advantage here: The torque (or shear stress, resp.) is kept constant and the hardening sample causes the resulting rotational speed (or shear rate, resp.) to decrease. Using the CSS mode, the continuing hardening process is disturbed less and less, and therefore, it is less influenced by the resulting decreasing degree of deformation. Finally, if the resistance force of the solid sample is larger than the shear force which is applicable by the test instrument, the rotational speed will be displayed as n = 0 (or as shear rate γ ̇ = 0, respectively). This indicates that the measuring system has come to a standstill after all.

      Note 2: Advantage of oscillatory tests when determining the gel point

      Nowadays, rotational tests should no longer be used for accurate investigations of processes such as gel formation, hardening or chemical curing reactions, since here, the process kinetics and reaction development, and therefore the test results, are often strongly influenced by the test conditions. Instead, oscillatory tests in the linear viscoelastic (LVE) deformation range should be performed since in this range, the user can be sure that the sample’s structure is strained only to a very limited extent, therefore remaining undestroyed during the whole test. Using this mode of testing, as well the onset of gel formation as well as the gel time can be exactly determined in the form of the sol/gel transition point (see Chapter 8.5.3b with Figure 8.36). A further advantage of oscillatory tests is the fact that the test can be still continued, even if the hardened material is already showing gel-like character, behavior of a soft or even of a rigid solid. In this case, viscosity values would be displayed as already “infinitely high”, being therefore no longer detectable by rotational tests at all. Further information